Sparsely encoded wireless data may be decoded using techniques such as message passing algorithm (MPA) or maximum likelihood sequence estimation (MLSE). Sparse code multiple access (SCMA) is one type of sparsely encoded data system proposed for multiple access in the next generation of mobile communication technology (often referred to as “5G”). Broadly speaking, SCMA is a coding technique that may enable non-orthogonal multiplexing of code layers, resource overloading, sparsity to reduce receiver complexity, multi-dimensional codewords, and spreading over multiple subcarriers. Non-orthogonal waveforms may facilitate a multiple access scheme in which sparse codewords of multiple layers of devices are overlaid in code and power domains and carried over shared time-frequency resources. Typically, the multiplexing of multiple devices may become overloaded if the number of overlaid layers is more than the length of the multiplexed codewords.
However, with SCMA, such overloading may be tolerable with moderate complexity of detection thanks to the reduced size of the SCMA multi-dimensional constellation and the sparseness of SCMA codewords. The sparse codewords enable the use of decoders with techniques, such as MPA or MLSE, to be used for detecting codewords from the combined codewords received by the decoders. The MPA and MLSE decoding techniques, however, may not provide the best solution to address concerns regarding complexity of decoding, latency or larger data sequences or codebooks.